A standard assumption adopted in the multi-armed bandit (MAB) framework is that the mean rewards are constant over time. This assumption can be restrictive in the business world as decision-makers often face an evolving environment where the mean rewards are time-varying. In this paper, we consider a non-stationary MAB model with $K$ arms whose mean rewards vary over time in a periodic manner. The unknown periods can be different across arms and scale with the length of the horizon $T$ polynomially. We propose a two-stage policy that combines the Fourier analysis with a confidence-bound-based learning procedure to learn the periods and minimize the regret. In stage one, the policy correctly estimates the periods of all arms with high probability. In stage two, the policy explores the periodic mean rewards of arms using the periods estimated in stage one and exploits the optimal arm in the long run. We show that our learning policy incurs a regret upper bound $\tilde{O}(\sqrt{T\sum_{k=1}^K T_k})$ where $T_k$ is the period of arm $k$. Moreover, we establish a general lower bound $Ω(\sqrt{T\max_{k}\{ T_k\}})$ for any policy. Therefore, our policy is near-optimal up to a factor of $\sqrt{K}$.
Universidade Federal de Lavras（拉夫拉斯联邦大学）；Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）
We address the problem of production planning and distribution in multi-echelon supply chains. We consider uncertain demands and lead times which makes the problem stochastic and non-linear. A Markov Decision Process formulation and a Non-linear Programming model are presented. As a sequential decision-making problem, Deep Reinforcement Learning (RL) is a possible solution approach. This type of technique has gained a lot of attention from Artificial Intelligence and Optimization communities in recent years. Considering the good results obtained with Deep RL approaches in different areas there…
Generating forecasts for time series with multiple seasonal cycles is an important use-case for many industries nowadays. Accounting for the multi-seasonal patterns becomes necessary to generate more accurate and meaningful forecasts in these contexts. In this paper, we propose Long Short-Term Memory Multi-Seasonal Net (LSTM-MSNet), a decomposition based, unified prediction framework to forecast time series with multiple seasonal patterns. The current state of the art in this space are typically univariate methods, in which the model parameters of each time series are estimated independently. …
IMT Lille Douai（里尔杜埃国立高等矿业电信学校）；Institut Mines-Télécom（法国国立高等矿业电信学院）；Univ. Lille（里尔大学）
Mining frequent episodes aims at recovering sequential patterns from temporal data sequences, which can then be used to predict the occurrence of related events in advance. On the other hand, gradual patterns that capture co-variation of complex attributes in the form of " when X increases/decreases, Y increases/decreases" play an important role in many real world applications where huge volumes of complex numerical data must be handled. Recently, these patterns have received attention from the data mining community exploring temporal data who proposed methods to automatically extract gradual …
Seoul National University（首尔大学）；Korea Aerospace University（韩国航空大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal autoregressive integrated moving average (SARIMA) models do not reflect the distinct characteristics of each period in seasonal patterns. We propose a mixed hierarchical seasonality (MHS) model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is taken. This results in a model that automatically le…
SANKEN Osaka University（大阪大学）；National University of Singapore（新加坡国立大学）
Given taxi-ride counts information between departure and destination locations, how can we forecast their future demands? In general, given a data stream of events with seasonal patterns that innovate over time, how can we effectively and efficiently forecast future events? In this paper, we propose Shifting Seasonal Matrix Factorization approach, namely SSMF, that can adaptively learn multiple seasonal patterns (called regimes), as well as switching between them. Our proposed method has the following properties: (a) it accurately forecasts future events by detecting regime shifts in seasonal …
North Carolina State University（北卡罗来纳州立大学）；Intuit AI（Intuit 人工智能）
Robust Anomaly Detection (AD) on time series data is a key component for monitoring many complex modern systems. These systems typically generate high-dimensional time series that can be highly noisy, seasonal, and inter-correlated. This paper explores some of the challenges in such data, and proposes a new approach that makes inroads towards increased robustness on seasonal and contaminated data, while providing a better root cause identification of anomalies. In particular, we propose the use of Robust Seasonal Multivariate Generative Adversarial Network (RSM-GAN) that extends recent advance…
North Carolina State University（北卡罗来纳州立大学）；Intuit Inc.（财捷公司）
Robust anomaly detection is a requirement for monitoring complex modern systems with applications such as cyber-security, fraud prevention, and maintenance. These systems generate multiple correlated time series that are highly seasonal and noisy. This paper presents a novel unsupervised deep learning architecture for multivariate time series anomaly detection, called Robust Seasonal Multivariate Generative Adversarial Network (RSM-GAN). It extends recent advancements in GANs with adoption of convolutional-LSTM layers and an attention mechanism to produce state-of-the-art performance. We condu…
In this work, we propose an ensemble forecasting approach based on randomized neural networks. Improved randomized learning streamlines the fitting abilities of individual learners by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach suitable for forecasting time series with multiple seasonality. We propose six strategies for controlling the diversity of ensemble members. Case studies conducted on four real-world forecasting problems verified the effectiveness and superior performanc…
Providing long-range forecasts is a fundamental challenge in time series modeling, which is only compounded by the challenge of having to form such forecasts when a time series has never previously been observed. The latter challenge is the time series version of the cold-start problem seen in recommender systems which, to our knowledge, has not been addressed in previous work. A similar problem occurs when a long range forecast is required after only observing a small number of time points --- a warm start forecast. With these aims in mind, we focus on forecasting seasonal profiles---or basel…
Pattern similarity-based methods are widely used in classification and regression problems. Repeated, similar-shaped cycles observed in seasonal time series encourage to apply these methods for forecasting. In this paper we use the pattern similarity-based methods for forecasting monthly electricity demand expressing annual seasonality. An integral part of the models is the time series representation using patterns of time series sequences. Pattern representation ensures the input and output data unification through trend filtering and variance equalization. Consequently, pattern representatio…
Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many seasonal-trend decomposition algorithms suffer from high computational cost and require a large amount of data when multiple seasonal components exist, especially when the periodic length is long. In this paper, we propose a general and efficient multi-scale seasonal-trend decomposition algorithm for time series with multiple seasonality. We first down-sample the origina…
Bus transit systems are the backbone of public transportation in the United States. An important indicator of the quality of service in such infrastructures is on-time performance at stops, with published transit schedules playing an integral role governing the level of success of the service. However there are relatively few optimization architectures leveraging stochastic search that focus on optimizing bus timetables with the objective of maximizing probability of bus arrivals at timepoints with delays within desired on-time ranges. In addition to this, there is a lack of substantial resear…
UC San Diego（加州大学圣地亚哥分校）；AWS AI Labs（亚马逊云科技人工智能实验室）；AWS（亚马逊云科技）
Transformer-based models have gained large popularity and demonstrated promising results in long-term time-series forecasting in recent years. In addition to learning attention in time domain, recent works also explore learning attention in frequency domains (e.g., Fourier domain, wavelet domain), given that seasonal patterns can be better captured in these domains. In this work, we seek to understand the relationships between attention models in different time and frequency domains. Theoretically, we show that attention models in different domains are equivalent under linear conditions (i.e.,…
Effective Series Decomposition and Components Learning for Time Series Generation
School of Engineering and Applied Science, University of Pennsylvania（工程与应用科学学院，宾夕法尼亚大学）；Viterbi School of Engineering, University of Southern California（工程学院，南加州大学）
TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Science and Technology of China（中国科学技术大学）
